Internal problem ID [6930]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 198.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Gegenbauer]
Solve \begin {gather*} \boxed {\left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +6 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 44
dsolve((1-t^2)*diff(y(t),t$2)-2*t*diff(y(t),t)+6*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} \left (-3 t^{2}+1\right )+c_{2} \left (\left (\frac {3 t^{2}}{8}-\frac {1}{8}\right ) \ln \left (t -1\right )+\left (-\frac {3 t^{2}}{8}+\frac {1}{8}\right ) \ln \left (t +1\right )+\frac {3 t}{4}\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 37
DSolve[(1-t^2)*y''[t]-2*t*y'[t]+6*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{2} \left (c_1 \left (3 t^2-1\right )+c_2 \left (3 t^2-1\right ) \tanh ^{-1}(t)-3 c_2 t\right ) \\ \end{align*}